Bond investors often like to buy shares in mutual funds that give returns that c
ID: 3333645 • Letter: B
Question
Bond investors often like to buy shares in mutual funds that give returns that closely follow commonly quoted indices, such as the blank index. One popular index is computed from several thousand different bond types. Roughly how many bonds do you think would be needed in a portfolio that could reliably give one year portfolio returns within half a percentage point of the index? You can assume bond returns typically vary in range from -5% to 5% with a standard deviation of about 2.5%, but state any other assumptions you make for this.
Explanation / Answer
Since the standard deviation is 2.5 % , And standard error is to be 0.5%
We can assume that we need the interval to be 95% confidence interval.
z of 95% Confidence interval = 1.96
1.96 * 2.5/sqrt(n) = 0.5
n = (1.96*5 )^2 = 9.8^2 = 96.04
We would need approximately 97 bonds to be within half a percentage point of the index with 95% confidence .